Question

radius ad intercepts circle a at point d. ray bc is tangent to the circle at d.
what is the measure of ∠bda?
use the keypad to enter your answer in the box. include the correct symbol for the units of measure.

Explanation:

Step1: Recall the tangent - radius theorem

The tangent - radius theorem states that a radius is perpendicular to the tangent at the point of tangency.

Step2: Determine the measure of ∠BDA

Since ray \(BC\) is tangent to the circle at \(D\) and \(AD\) is the radius, by the tangent - radius theorem, \(AD\perp BC\). When two lines are perpendicular, the angle between them is \(90^{\circ}\). So, \(\angle BDA = 90^{\circ}\).

Answer:

\(90^{\circ}\)